Ratio and proportion — Paper 4 · IGCSE Mathematics (9-1) 0980

1 (a) The price of a newspaper increased from $0.97 to $1.13 . Calculate the percentage increase. … % [3] (b) One day, the newspaper had 60 pages of news and advertisements. The ratio number of pages of news : number of pages of advertisements = 5 : 7. (i) Calculate the number of pages of advertisements. … [2] (ii) Write the number of pages of advertisements as a percentage of the number of pages of news. … % [1] (c) On holiday Maria paid 2.25 euros for the newspaper when the exchange rate was $1 = 0.9416 euros. At home Maria paid $1.13 for the newspaper. Calculate the difference in price. Give your answer in dollars, correct to the nearest cent. $ … [3] (d) The number of newspapers sold decreases exponentially by x% each year. Over a period of 21 years the number of newspapers sold decreases from 1 763 000 to 58 000. Calculate the value of x. x = … [3] (e) Every page of the newspaper is a rectangle measuring 43 cm by 28 cm, both correct to the nearest centimetre. Calculate the upper bound of the area of a page. … cm2 [2]

14 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 16.5 or 16.49... 3 M2 for 1.13 − 0.97[× 100] oe or 1.13 × 100 oe 0.97 0.97 1.13 or M1 for oe 0.97 1(b)(i) 35 2 M1 for 60 ÷ ( 5 + 7 ) 1(b)(ii) 140 1 1(c) $1.26 final answer 3 B2 for 1.259... or 1.26 but not as final answer or M1 for 2.25 ÷ 0.9416 If 0 scored, SC1 for 1.13 × 0.9416 1(d) 15[.0…] 3 58000 M2 for 21 oe 1763000 or M1 for 58000 = 1763000 ( k ) 21 1(e) 1239.75 2 B1 for 43 + 0.5 or 28 + 0.5 oe seen

This question in 0980/42 May/June 2019

2 (a) Ali and Mo share a sum of money in the ratio Ali : Mo = 9 : 7. Ali receives $600 more than Mo. Calculate how much each receives. Ali $ … Mo $ … [3] (b) In a sale, Ali buys a television for $195.80 . The original price was $220. Calculate the percentage reduction on the original price. … % [3] (c) In the sale, Mo buys a jacket for $63. The original price was reduced by 25%. Calculate the original price of the jacket. $ … [3]

9 marks

Mark scheme: 2(a) [Ali] 2700 3 B2 for one correct or for correct values [Mo] 2100 reversed or M1 for 600 ÷ (9 – 7) or for any equation that would lead to an answer of 300, 2700 or 2100, or 4800 (for the total) 2(b) 11 3 220 − 1958. M2 for [× 100] or for 220 1958. [100 − ] × 100 220 195 8. or M1 for 220 – 195.8 or for or a 220 correct implicit equation for percentage 195.8 − 220 reduction or for 220 2(c) 84 3 63 M2 for oe 25 1 − 100 or M1 for associating 63 with (100 – 25)% or a correct implicit equation for the original price.

This question in 0980/41 Oct/Nov 2019

1 (a) (i) Divide $24 in the ratio 7 : 5. $ … , $ … [2] (ii) Write $24.60 as a fraction of $2870. Give your answer in its lowest terms. … [2] (iii) Write $1.92 as a percentage of $1.60 . … % [1] (b) In a sale the original prices are reduced by 15%. (i) Calculate the sale price of a book that has an original price of $12. $ … [2] (ii) Calculate the original price of a jacket that has a sale price of $38.25 . $ … [2] (c) (i) Dean invests $500 for 10 years at a rate of 1.7% per year simple interest. Calculate the total interest earned during the 10 years. $ … [2] (ii) Ollie invests $200 at a rate of 0.0035% per day compound interest. Calculate the value of Ollie’s investment at the end of 1 year. [1 year = 365 days.] $ … [2] (iii) Edna invests $500 at a rate of r % per year compound interest. At the end of 6 years, the value of Edna’s investment is $559.78 . Find the value of r. r = … [3]

16 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 14, 10 2 M1 for 24 ÷ (7 + 5) 1(a)(ii) 3 2 B1 for correct fraction not in lowest terms 350 1(a)(iii) 120 1 1(b)(i) 10.2[0] 2 15 M1 for × 12 oe or better 100 1(b)(ii) 45 2 38.25 M1 for oe 15 1 − 100 1(c)(i) 85 2 500 × 1.7 × 10 M1 for oe 100 1(c)(ii) 203 or 202.5 to 202.6 2 365  0.0035  M1 for 200 ×  1 +   100  1(c)(iii) 1.9 3 559.78 M2 for 6 500  r 6 or M1 for 500  1 +  = 559.78  100 

This question in 0980/42 May/June 2020

2 (a) A plane has 14 First Class seats, 70 Premium seats and 168 Economy seats. Find the ratio First Class seats : Premium seats : Economy seats. Give your answer in its simplest form. … : … : … [2] (b) (i) For a morning flight, the costs of tickets are in the ratio First Class : Premium : Economy = 14 : 6 : 5. The cost of a Premium ticket is $114. Calculate the cost of a First Class ticket and the cost of an Economy ticket. First Class $ … Economy $ … [3] (ii) For an afternoon flight, the cost of a Premium ticket is reduced from $114 to $96.90 . Calculate the percentage reduction in the cost of a ticket. … % [2] (c) When the local time in Athens is 09 00, the local time in Berlin is 08 00. A plane leaves Athens at 13 15. It arrives in Berlin at 15 05 local time. (i) Find the flight time from Athens to Berlin. … h … min [1] (ii) The distance the plane flies from Athens to Berlin is 1802 km. Calculate the average speed of the plane. Give your answer in kilometres per hour. … km/h [2]

10 marks

Mark scheme: 2(a) 1 : 5 : 12 2 1 5 12 M1 for 2 : 10 : 24 or 7 : 35 : 84 or : : 18 18 18 2(b)(i) 266 and 95 3 B2 for 266 or 95 or 266 and 95 reversed 114 or M1 for 6 2(b)(ii) 15 2 114 − 96.9 M1 for [× 100] oe 114 96.9 or × 100 114 2(c)(i) 2h 50min 1 2(c)(ii) 636 2 M1 for 1802 ÷ their 2h 50min

This question in 0980/41 Oct/Nov 2020

1 (a) A 2.5-litre tin of paint costs $13.50 . In a sale, the cost is reduced by 14%. (i) Work out the sale price of this tin of paint. $ … [2] (ii) Work out the cost of buying 42.5 litres of paint at this sale price. $ … [2] (b) Henri buys some paint in the ratio red paint : white paint : green paint = 2 : 8 : 5. (i) Find the percentage of this paint that is white. … % [1] (ii) Henri buys a total of 22.5 litres of paint. Find the number of litres of green paint he buys. … litres [2] (c) Maria paints a rectangular wall. The length of the wall is 20.5 m and the height is 2.4 m, both correct to 1 decimal place. One litre of paint covers an area of exactly 10 m2. Calculate the smallest number of 2.5-litre tins of paint she will need to be sure all the wall is painted. Show all your working. … [4]

11 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 11.61 final answer 2  14  M1 for 13.5[0] ×  1 −  oe  100  or B1 for 1.89 1(a)(ii) 197.37 final answer 2 FT 17 × their (a)(i) exact or correct to nearest cent M1 for 42.5 ÷ 2.5 1(b)(i) 53.3 or 53.33… 1 1(b)(ii) 7.5 2 M1 for 22.5 ÷ (2 + 8 + 5) oe soi 1(c) 20.55 × 2.45 oe M2 M1 for 20.5 + 0.05 oe seen or 2.4 + 0.05 oe seen If 0 scored, SC1 here for 20.45 × 2.35 oe 3 nfww A2 M1 for their area ÷ 10 ÷ 2.5 oe

This question in 0980/42 May/June 2021

8 (a) A cuboid has length L cm, width W cm and height H cm. L cm H cm NOT TO SCALE 20.1 cm W cm 37.8 cm The diagram shows the net of this cuboid. The ratio W : L = 1 : 2. Find the value of L, the value of W and the value of H. L = … W = … H = … [5] (b) E NOT TO SCALE 24 cm D C 15 cm A 18 cm B The diagram shows a solid pyramid with a rectangular base ABCD. E is vertically above D. Angle EDC = angle EDA = 90°. AB = 18 cm, BC = 15 cm and EC = 24 cm. (i) The pyramid is made of wood and has a mass of 800 g. Calculate the density of the wood. Give the units of your answer. 1 [The volume, V, of a pyramid is V = # area of base # height.] 3 [Density = mass ' volume] … … [5] (ii) Calculate the angle between BE and the base of the pyramid.

14 marks

Mark scheme: 8(a) [L =] 11.8 5 M1 for L = 2W oe soi [W =] 5.9 M1 for W + 2H = 20.1 oe [H =] 7.1 M1 for 2L + 2H = 37.8 oe B1 for at least one correct answer 8(b)(i) 0.559 to 0.56[0…] B4 1 2 2 M2 for × 18 × 15 × 24 − 18 isw 3 conversion or M1 for h2 + 182 = 242 oe or better M1 for figs 800 ÷ figs their volume isw g/cm3 or g cm–3 final answer B1 8(b)(ii) 34.1 or 34.11 to 34.12 4 2 2 24 − 18 M3 for tan [ ] = oe 18 2 + 15 2 or M2 for 18 2 + 15 2 isw or 24 2 + 15 2 isw or M1 for 182 + 152 isw or 242 + 152 isw or M1 for indicating required angle is EBD

This question in 0980/42 May/June 2021

2 Bob, Chao and Mei take part in a run for charity. (a) Their times to complete the run are in the ratio Bob : Chao : Mei = 4 : 5 : 7. (i) Find Chao’s time as a percentage of Mei’s time. … % [1] (ii) Bob’s time for the run is 55 minutes 40 seconds. Find Mei’s time for the run. Give your answer in minutes and seconds. … min … s [3] (b) Chao collects $47.50 for charity. (i) Bob collects 28% more than Chao. Find the amount Bob collects. $ … [2] (ii) Chao collects 60% less than Mei. Find how much more money Mei collects than Chao. $ … [3] (c) When running, Chao has a stride length of 70 cm, correct to the nearest 5 cm. Chao runs a distance of 11.2 km, correct to the nearest 0.1 km. Work out the minimum number of strides that Chao could take to complete this distance. … [4] (d) In 2015, a charity raised a total of $1.6 million. After 2015, this amount increased exponentially by 2.4% each year for the next 5 years. Work out the amount raised by the charity in 2020. $ … million [2]

15 marks

Mark scheme: 2(a)(i) 71.4 or 71.42 to 71.43 1 2(a)(ii) 97 [min] 25 [s] 3 B2 for 13 min 55 sec seen or 97.4 or 97.41 to 97.42 seen or 5845 seen OR M2 for 55.66… ÷ 4 × 7 oe or 3340 ÷ 4 × 7 oe or for 7/4 × 55 + 7/4 × 40 oe or M1 for 55 min 40 sec ÷ 4 oe or M1 for total time ÷ 16 soi 2(b)(i) 60.8[0] 2  28  M1 for 47.5 ×  1 +  oe  100  or B1 for 13.3[0] 2(b)(ii) 71.25 3 B2 for 118.75  60  Or M2 for 47.50 ÷  1 −  – 47.50  100   60  or M1 for x ×  1 −  = 47.50 oe or  100  better 2(c) 15 380 4 M3 for (1 120 000 – 5000) ÷ (70 + 2.5) oe or B2 for answer figs 15 379 to figs 15 380 or M2 for (1 120 000 ± 5000) ÷ (70 ± 2.5) oe or M1 for one of figs 675, 725, 1115, 1125 seen 2(d) 1.8[0] or 1.801 to 1.802 [million] nfww 2 5  2.4  M1 for figs 16 ×  1 +  oe  100 

This question in 0980/41 Oct/Nov 2021

1 (a) Find the lowest common multiple (LCM) of 30 and 75. … [2] (b) Share $608 in the ratio 4 : 5 : 7. $ … $ … $ … [3] 6 .39 # 10 4 (c) Work out 6 . 2 .45 # 10 Give your answer in standard form. … [2] (d) Write .027o o as a fraction. … [1] (e) A stone has volume 45 cm 3 and mass 126 g. Find the density of the stone, giving the units of your answer. [Density = mass ' volume] … … [2]

10 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 150 2 B1 for answer 150k or M1 for prime factors of 30 or 75 seen or a list of multiples of both 30 and 75 with at least 3 of each 30  75 or for oe 15 or for answer 2  3  52 1(b) 152 3 Accept in any order B2 for two correct answers 190 608 or M1 for  k oe where k =1, 4, 5, 7 4  5  7 266 1(c) 2.61  10–2 2.61  10 2 or 2 B1 for figs 2608 or 261 seen 2.608…  10–2 If 0 scored, SC1 for answer 2.6[0]  10–2 without more accurate value in standard form seen 1(d) 27 1 oe fraction 99 1(e) 2.8 1 g/cm3 or g cm–3 1

This question in 0980/42 May/June 2022

6 (a) At a festival, 380 people out of 500 people questioned say that they are camping. There are 55 300 people at the festival. Calculate an estimate of the total number of people camping at the festival. … [2] (b) 12 friends travel to the festival. 5 travel by car, 4 travel by bus and 3 travel by train. Two people are chosen at random from the 12 friends. Calculate the probability that they travel by different types of transport. … [4] (c) Arno buys a student ticket for $43.68 . This is a saving of 16% on the full price of a ticket. Calculate the full price of a ticket. $ … [2] (d) At a football match, there are 29 800 people, correct to the nearest 100. (i) At the end of the football match, the people leave at a rate of 400 people per minute, correct to the nearest 50 people. Calculate the lower bound for the number of minutes it takes for all the people to leave. … min [3] (ii) At a cricket match there are 27 500 people, correct to the nearest 100. Calculate the upper bound for the difference between the number of people at the football match and at the cricket match. … [2]

13 marks

Mark scheme: 6(a) 42 028 2 380 M1 for oe soi isw 500 6(b) 47 4 0.712[1…] oe 66  5 4   4 3   5 3  M3 for 2   2   2         12 11   12 11   12 11  oe  5 4 4 3 3 2  or 1 –      oe    12 11 12 11 12 11  or M2 for sum of 3 or more correct product pairs and no incorrect pairs 5 4 4 3 3 2 or for      and no other 12 11 12 11 12 11 pairs k j or M1 for  seen 12 11 94 If 0 scored SC1 for answer oe 144 6(c) 52 2 100  16 M1 for x   43.68 oe or better 100 6(d)(i) 70 or 70.16[5…] or 70.17 or 70.2 3 29750 to 29800 29750 to 29800 M2 for or or 400  25 400  24 29800  50 400to425 or B1 for 29 750 or 29 850 or 29 849 or 375 or 425 or 424 seen 6(d)(ii) 2399 2 B1 for 27 450 or 27 550 or 27 549 or 29 850 or or 2400 nfww 29 849 seen

This question in 0980/42 May/June 2022

1 (a) 42° NOT TO SCALE x° The diagram shows an isosceles triangle with the base extended. Find the value of x. x = … [3] (b) The diagram shows three lines meeting at a point. The ratio a : b : c = 3 : 4 : 5. Find the value of c. a° NOT TO c° b° SCALE c = … [3] (c) A regular pentagon has an exterior angle, d. A regular hexagon has an interior angle, h. d Find the fraction . h Give your answer in its simplest form. … [4] (d) S R x° ( x + 20)° NOT TO SCALE ( 3x – 40)° Q ( 2x – 5)° P Show that PQRS is a cyclic quadrilateral. [5] (e) B A 50° 9 cm NOT TO O SCALE The diagram shows a circle of radius 9 cm, centre O. The minor sector AOB, with sector angle 50°, is removed from the circle. Calculate the length of the major arc AB. … cm [3]

18 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 111 3  42 M2 for 180 –180 oe or 42 + 2 180  42 oe 2 180  42 or M1 for oe 2 1(b) 150 3 M1 for k ÷ (3 + 4 + 5) [×p] where p = 1, 3, 4 or 5 5 or oe 12 B1 for 360 used 1(c) 3 4 72 cao nfww B3 for 5 120 or B2 for [d = ] 72 or [h = ] 120 or M1 for 360 ÷ 5 oe isw or 180 – (360 ÷ 6) isw or for (6 – 2) × 180 [÷ 6] 1(d) x + 2x – 5 + x + 20 + 3x – 40 = 360 M1 Accept equivalent equation e.g. 7x – 25 = 360 7x = 360 + 5 – 20 + 40 or better M1 FT their equation, accept e.g. 7x = 385 x = 55 B1 55 and 125 B1dep Dep on M1M1B1 or 105 and 75 Accept 55 + 3 × 55 – 40 = 180 or 2 × 55 – 5 + 55 + 20 = 180 If B0 scored, SC1 for 55, 75, 105 and 125 Opposite angles sum to 180 oe A1 Dep on M1M1B1B1 [so PQRS is a cyclic quadrilateral ] 1(e) 48.7 or 48.69 to 48.70… 3 360  50 M2 for 2 π oe9 360 50 or M1 for  2  π oe9 360

This question in 0980/42 May/June 2023

1 (a) A fruit drink is made using 1.5 litres of apple juice and 450 millilitres of mango juice. Write the ratio apple juice : mango juice in its simplest form. … : … [2] (b) One litre of fruit drink is shared between three cups. The amount in the cups is in the ratio 9 : 6 : 10. Calculate the number of millilitres in each cup. … ml , … ml , … ml [3] (c) A shop buys bottles of the fruit drink for $3.20 each. It sells them at a profit of 15%. Calculate the selling price of each bottle of fruit drink. $ … [2] (d) The number of bottles of fruit drink sold has grown exponentially at a constant rate of 2.5% per year. 5 years ago, the shop sold 16 620 bottles. Calculate the number of bottles sold this year. … [2] (e) d cm NOT TO 23 cm SCALE 18.5 cm The bottles of juice are 18.5 cm tall, correct to the nearest millimetre. They are stored on shelves. The distance between the shelves is 23 cm, correct to the nearest centimetre. Calculate the lower bound for the distance, d cm, between the top of a bottle and the shelf above it. … cm [3]

12 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 10 : 3 final answer 2 M1 for 1500 : 450 oe in ratio form If 0 scored SC1 for answer 3 : 10 1(b) 360 240 400 3 B2 for answer 0.36 0.24 0.4 or for answer two of 360 240 400 1000 or M1 for [ k ] where k = 1, 9, 9  6  10 6 or 10 If 0 scored, SC1 for answer with 3 values in ratio 9 : 6 : 10 in that order 1(c) 3.68 cao 2  15  M1 for  1    3.2 oe  100  or B1 for answer 0.48 1(d) 18 804[.0...] 2  2.5  5 1 for 16620   1   oe  100  1(e) 3.95 3 M2 for 22.5 – (18.5 to 18.6) or (22 to 23) −18.55 or M1 for 23 – 0.5 oe seen or 23 + 0.5 oe seen or 18.5– 0.05 oe seen or 18.5 + 0.05 oe seen

This question in 0980/42 May/June 2024

4 (a) Enzo, Rashid and Blessy each swim as many lengths of a swimming pool as they can in 15 minutes. The results are shown in the table. Name Number of lengths Enzo 11.25 Rashid 18.75 Blessy 20 (i) Find the number of lengths Enzo swims as a percentage of the total number of lengths all three people swim. … % [2] (ii) Write the ratio of the number of lengths each person swims in the form Enzo : Rashid : Blessy. Give your answer in its simplest form. … : … : … [2] (iii) Each length of the pool is 25 m. (a) Work out Blessy’s average swimming speed for the 15 minutes. Give your answer in metres per second. … m/s [3] (b) Rashid continues to swim at the same rate. Calculate the time it takes Rashid to swim a total distance of 5 km. Give your answer in hours and minutes. … h … min [4] (iv) Blessy swims for one hour. The number of lengths she swims decreases by 5% every 15 minutes. Calculate the number of lengths she swims in the final 15 minutes. … [3] (b) Another swimmer, Adam, swims 450 m, correct to the nearest 25 metres. This takes 10 minutes, correct to the nearest minute. Calculate the minimum distance Adam swims in one hour at this rate. … m [3]

17 marks

Mark scheme: 4(a)(i) 22.5 2 11.25 M1 for 100  oe 11.25 + 18.75 + 20 4(a)(ii) 9 : 15 : 16 2 M1 for 1125 : 1850 : 2000 or better 4(a)(iii)(a) 5 3 or 0.556 or 0.5555 to 0.5556 9 20  25 M2 for oe 15[ 60] or M1 for 20 × 25 or for their distance ÷ (15 [× 60]) oe 4(a)(iii)(b) 2 h 40 mins 4 Approach 1 8 B3 for [h]oe or 160 [mins] or 9600[s] 3 Or M3 for 5000 ÷ (18.75 × 25 × 4)[h] oe or 5000 ÷ (18.75 × 25 ÷ 15)[mins] oe or 5000 ÷ ((18.75 × 25 × 4) ÷ (60 × 60))[secs] oe Or M2 for (18.75 × 25 × 4)[m/h] oe or (18.75 × 25 ÷ 15)[m/min] oe or (18.75 × 25 × 4) ÷ (60 × 60))[m/sec] oe Or B1 for 200 or 1 km =1000m soi After 0 scored SC1 for time Figs 267 or figs 2666 to 2667 or figs 16 or figs 96 Approach 2 B3 for 160 [mins] Or M3 for 15 × 5000 ÷ (18.75 × 25) [mins] oe Or M2 for 5000 ÷ (18.75 × 25) oe Or B1 for 200 or 1 km =1000m soi After 0 scored SC1 for time figs 16 4(a)(iv) 17.1 or 17.14 to 17.15 3 3  100 − 5  M2 for 20 ×   oe  100   100 − 5  k or M1 for 20 ×   where k is 2, or  100  4  100 − 5  3 or for 20 ×   oe seen and spoiled  100  4(b) 2500 3 425to450 450 − 12.5 M2 for or or 10 + 0.5 10 to 11 425 to 450 450 − 12.5 or 630 600 to 660 or M1 for 10.5 or 9.5 or 437.5 or 462.5 or 630[s] or 570[s]

This question in 0980/41 Oct/Nov 2024

3 Mass of box A : Mass of box B = 4 : 7 The mass of box B is 2.4 kg more than the mass of box A. Calculate the mass of box A and the mass of box B. box A … kg box B … kg [3]

3 marks

Mark scheme: 3 [A =] 3.2 3 B2 for one correct or for both correct but [B =] 5.6 reversed 2.4 or M1 for  k where k = 1, 4, 7 or 11 oe 7 − 4 x 4 or for = oe x + 2.4 7

This question in 0980/42 May/June 2025